publication date

  • January 2018

start page

  • 1913

end page

  • 1930


  • 78

International Standard Serial Number (ISSN)

  • 0036-1399

Electronic International Standard Serial Number (EISSN)

  • 1095-712X


  • This paper addresses the heating of a gas confined in a closed vessel whose wall temperature changes with a time scale much longer than the vessel acoustic time, so that the relative spatial pressure variations remain small at all times. The solution must account for the induced gas motion as well as for the temporal variation of the nearly uniform pressure. Specific attention is given to transients in centrally symmetric vessels following a rapid change of the wall temperature to a prescribed constant value. For times much smaller than the vessel conduction time t'(c) the direct effects of heat conduction are confined to a near-wall boundary layer where we find large transverse velocities associated with the thermal expansion. The edge of the boundary layer acts as a piston for the isentropic core region, where the thermodynamic properties remain spatially uniform. For a given wall temperature, the solution involves a nonlinear eigenvalue problem, whose integration provides the initial evolution of the pressure and of the heat-transfer rate, which are independent of the vessel shape at leading order. Simplified solutions are obtained for wall temperatures that are either much smaller or much larger than the initial gas temperature, with the latter case displaying front solutions in which the edge of the thermal wave becomes a contact surface. Complete transient histories for times of order t'(c) are computed for planar, cylindrical, and spherical geometries including heating/cooling processes for wall temperatures that are larger/smaller than the initial temperature. Asymptotic predictions are obtained for times much larger than the vessel conduction time, when the temperature departures from the wall value are everywhere small, thereby enabling a closed-form analytic expression for the temperature distribution to be derived based on the linearized form of the conservation equations.


  • nonlinear heat conduction; matched asymptotic expansions; front solutions